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Timed writing: Mathematics and me

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The earliest positive memory I have of math is when during a tutoring session when I was around grade 1. I vaguely remember scoring a perfect on my test and getting to write my name on the star board. From that point, I remember being very confident in my math abilities throughout elementary. My parents would say I had a 'talent' in math. I believe it was around grade 7 where I started learning about integers and I was struggling. This was the first time I had ever struggled with a math concept. I remember having to redo the test around 2 or 3 times until I finally understood the material. This led me to understand that even though I was strong in other math areas, there were some topics that I would not grasp.  I believe that failure has humbled me as a student and gave me a new perspective on math education. As I got into high school, I quickly realized that I was not the only one who was good at math. There were many other students who I thought were much smarter than me. ...
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Instrumental vs. Relational

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Richard Skemp describes instrumental understanding as 'rules without reason'. When he was giving such examples in math, it made me think of my time as a student in high school. I remember learning trigonometric identities and using them to solve problems, but I didn't understand what  they truly meant. I did not understand where  they came from and why   we used them, I only understood how  to apply them. This is the main difference between what Skemp describes as relational vs. instrumental understanding. Relational understanding answers why,  whereas instrumental only answers  how . Skemp tells us of these mathematical mis-matches, where the student's goal is to understand instrumentally, while being taught by a teacher wants them to understand relationally. Up until grade 10, I was one of these students who only had a instrumental understanding of mathematics. I had an amazing teacher who taught us in this relational way of understanding. This teacher ...
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